Singularly perturbed control law for linear time-invariant delay SISO systems

This paper considers the problem of stabilizing a single-input single-output linear time-invariant delay system, where the parameters of the system are unknown. Using norm bounds of the unknown parameters, a low-order controller and reference model are proposed. The closed-loop system is a linear singularly perturbed retarded system with uniform asymptotic stability behavior. We calculate bounds \(\varepsilon \in (0,\varepsilon ^{*})\) as in the book of Kokotovic, Khalil and O’Reilly, such that the uniform asymptotic stability of the linear singularly perturbed delay system is guaranteed. We show how to design a control law such that the system dynamics is assigned by a Hurwitz polynomial with constant coefficients.